# yI1-xI1-related-EMWproposal.R
# Philips, Andrew Q. "How to Avoid Incorrect Inference (While Gaining Correct Ones) in Dynamic Models". Forthcoming at Political Science Research and Methods. 
# andrew.philips@colorado.edu 
# 2/9/21
#
# Figures produced in this R script:
#   --SI, Figure 38: "yi1-xi1-related-emwproposal.pdf"
# -----------------------------------

# -----------------------------------
# EXPERIMENT 6: Y ~ I(1), X ~ I(1), AND cointegrating
# Type II error
# ONLY CALCULATING THE LRE IF L.X (ARDL/ECM) AND X (LDV) ARE FIRST STAT SIG (to appear in SI)
# -----------------------------------
rm(list = ls())
setwd("~/Dropbox/My_Folder/Papers-Projects/Wlezien-Enns-PSRM/Final-Feb2021/scripts/")
# -----------------------------------
library(dynamac)
library(nlWaldTest)
library(ggplot2)
library(grid)
library(gridExtra)
library(dplyr)

set.seed(01902010)
# -------------------------------------------------------------
# EXPERIMENT 6: Y ~ I(1), X ~ I(1), AND cointegrating
sims = 2000 # no. sims
N <- c(50, 250, 1000) # number of obs
e.var <- c(1, 5) # error variance in Y
B.dx.true = 2
B.lx.true = c(1, -1)
phi.true = c(-0.2, -0.8)
# so LRMs are:
B.lx.true[1]/-phi.true[1]
B.lx.true[1]/-phi.true[2]
B.lx.true[2]/-phi.true[1]
B.lx.true[2]/-phi.true[2]

container.ardl <- matrix(NA, nrow = sims*length(N)*length(e.var)*length(phi.true)*length(B.lx.true), ncol = 11) # null matrix to hold output
# cols = sims, N, Beta.lx, UL.beta.lx, LL.beta.lx, LR.x, LR.x.UL, LR.x.LL, e.var, phi.true, B.lx.true
container.ecm <- matrix(NA, nrow = sims*length(N)*length(e.var)*length(phi.true)*length(B.lx.true), ncol = 11) # null matrix to hold output
# cols = sims, N, Beta.lx, UL.beta.lx, LL.beta.lx, LR.x, LR.x.UL, LR.x.LL, e.var, phi.true, B.lx.true
container.ldv <- matrix(NA, nrow = sims*length(N)*length(e.var)*length(phi.true)*length(B.lx.true), ncol = 11) # null matrix to hold output
# cols = sims, N, Beta.lx, UL.beta.lx, LL.beta.lx, LR.x, LR.x.UL, LR.x.LL, e.var, phi.true, B.lx.true
# -------------------------------------------------------------

row <- 1
prog <- txtProgressBar(min = 0, max = sims, style = 3)
for (s in 1:sims) {
  for (n in N) {
    for (ev in e.var) {
      for (p in phi.true) {
        for (b in B.lx.true) {
          setTxtProgressBar(prog, value = s)
          
          x.error <- rnorm(n + 100, sd = 1)
          x <- x.error
          y.error <- rnorm(n + 100, sd = sqrt(ev))
          y <- y.error
          y.diff <- rep(NA, length(y))
          for(i in 2:length(x)) {
            x[i] <- x[i-1] + x.error[i]
            y.diff[i] <- p*y[i-1] + B.dx.true*(x[i] - x[i-1]) + b*x[i-1] + y.error[i]
            y[i] <- y[i-1] + y.diff[i]
          }
          
          # ARDL model:
          res.ardl <- lm(y[101:length(y)] ~ lshift(y, 1)[101:length(y)] + x[101:length(x)] + lshift(x, 1)[101:length(x)])
          # ECM model:
          res.ecm <- lm(dshift(y)[101:length(y)] ~ lshift(y, 1)[101:length(y)] + dshift(x)[101:length(x)] + lshift(x, 1)[101:length(x)])
          # LDV model
          res.ldv <- lm(y[101:length(y)] ~ lshift(y, 1)[101:length(y)] + x[101:length(x)])
          
          # grab QOI (FORALL): ----
          container.ardl[row, 1] <- container.ecm[row, 1] <- container.ldv[row, 1] <- s # no sims
          container.ardl[row, 2] <- container.ecm[row, 2] <- container.ldv[row, 2] <- n # T
          container.ardl[row, 9] <- container.ecm[row, 9] <- container.ldv[row, 9] <- ev # error variance of Y
          container.ardl[row, 10] <- container.ecm[row, 10] <- container.ldv[row, 10] <- p # true value of phi
          container.ardl[row, 11] <- container.ecm[row, 11] <- container.ldv[row, 11] <- b # true value of effect of l.x
          
          # QOI (ARDL)
          container.ardl[row, 3] <- coef(res.ardl)[4] # beta.lx
          container.ardl[row, 4] <- confint.default(res.ardl, parm = c(4), level = 0.95)[2] # UL
          container.ardl[row, 5] <- confint.default(res.ardl, parm = c(4), level = 0.95)[1] # LL
          # LR effects (ARDL)
          lrm <- nlConfint(res.ardl, "(a[3] + a[4])/(1-a[2])", level = 0.95)
          container.ardl[row, 6] <- lrm[1] # LRM
          container.ardl[row, 7] <- lrm[3] # LRM UL
          container.ardl[row, 8] <- lrm[2] # LRM LL
          
          # QOI (ECM)
          container.ecm[row, 3] <- coef(res.ecm)[4] # beta.l.x
          container.ecm[row, 4] <- confint.default(res.ecm, parm = c(4), level = 0.95)[2] # UL
          container.ecm[row, 5] <- confint.default(res.ecm, parm = c(4), level = 0.95)[1] # LL
          # LR effects (ECM)
          lrm <- nlConfint(res.ecm, "(a[4])/(-a[2])", level = 0.95)
          container.ecm[row, 6] <- lrm[1] # LRM
          container.ecm[row, 7] <- lrm[3] # LRM UL
          container.ecm[row, 8] <- lrm[2] # LRM LL
          
          # QOI (LDV)
          container.ldv[row, 3] <- coef(res.ldv)[3]
          container.ldv[row, 4] <- confint.default(res.ldv, parm = c(3), level = 0.95)[2] # UL
          container.ldv[row, 5] <- confint.default(res.ldv, parm = c(3), level = 0.95)[1] # LL
          # LR effects (LDV)
          lrm <- nlConfint(res.ldv, "(a[3])/(1-a[2])", level = 0.95)
          container.ldv[row, 6] <- lrm[1] # LRM
          container.ldv[row, 7] <- lrm[3] # LRM UL
          container.ldv[row, 8] <- lrm[2] # LRM LL
          
          row <- row + 1
        } # close l.x Beta loop
      } # close phi loop
    } # close error var loop
  } # close N loop
} # close sim loop

#save.image("scenario-yi1-xi1-cointegrating-EMWproposal-data.RData")
#load("scenario-yi1-xi1-cointegrating-EMWproposal-data.RData")

# Create rejection rates and label:
container.ardl <- as.data.frame(container.ardl)
# cols = sim, N, Beta.lx, UL.beta.lx, LL.beta.lx, LR.x, LR.x.UL, LR.x.LL, e.var, phi, B.lx.true
colnames(container.ardl) <- c("sims", "Time", "Beta.lx", "Beta.lx.ul", "Beta.lx.ll", "LR.x", "LR.x.UL", "LR.x.LL", "e.var", "phi", "B.lx.true")
container.ecm <- as.data.frame(container.ecm)
# cols = sim, N, Beta.lx, UL.beta.lx, LL.beta.lx, LR.x, LR.x.UL, LR.x.LL, e.var, phi, B.lx.true
colnames(container.ecm) <- c("sims", "Time", "Beta.lx", "Beta.lx.ul", "Beta.lx.ll", "LR.x", "LR.x.UL", "LR.x.LL", "e.var", "phi", "B.lx.true")
container.ldv <- as.data.frame(container.ldv)
# cols = sim, N, Beta.x, UL.beta.x, LL.beta.x, LR.x, LR.x.UL, LR.x.LL, e.var, phi, B.lx.true
colnames(container.ldv) <- c("sims", "Time", "Beta.x", "Beta.x.ul", "Beta.x.ll", "LR.x", "LR.x.UL", "LR.x.LL", "e.var", "phi", "B.lx.true")

# proportion rejecting beta.lx = 0 (ARDL/ECM) or beta.x = 0 (LDV)
container.ardl$reject.beta.lx <- ifelse(container.ardl$Beta.lx.ll > 0 | container.ardl$Beta.lx.ul < 0, 1, 0)
container.ecm$reject.beta.lx <- ifelse(container.ecm$Beta.lx.ll > 0 | container.ecm$Beta.lx.ul < 0, 1, 0)
container.ldv$reject.beta.x <- ifelse(container.ldv$Beta.x.ll > 0 | container.ldv$Beta.x.ul < 0, 1, 0)

# proportion rejection, LR (from truth; i.e., = 1 if constructed 95% CI's DON'T encompass true LRM):
container.ardl$reject.lrm.truth <- ifelse(container.ardl$LR.x.LL > ((container.ardl$B.lx.true)/(-container.ardl$phi)) | container.ardl$LR.x.UL < ((container.ardl$B.lx.true)/(-container.ardl$phi)), 1, 0)
container.ecm$reject.lrm.truth <- ifelse(container.ecm$LR.x.LL > ((container.ecm$B.lx.true)/(-container.ecm$phi)) | container.ecm$LR.x.UL < ((container.ecm$B.lx.true)/(-container.ecm$phi)), 1, 0)
container.ldv$reject.lrm.truth <- ifelse(container.ldv$LR.x.LL > ((container.ldv$B.lx.true)/(-container.ldv$phi)) | container.ldv$LR.x.UL < ((container.ldv$B.lx.true)/(-container.ldv$phi)), 1, 0)

# Coding of rejection of LRM:
# = 1 if we reject LRM = truth AND also reject beta.lx/beta.x = 0, 0 otherwise
container.ardl$reject.lrm.yes.lx <- ifelse(container.ardl$reject.lrm.truth == 1 & container.ardl$reject.beta.lx == 1, 1, 0)
container.ecm$reject.lrm.yes.lx <- ifelse(container.ecm$reject.lrm.truth == 1 & container.ecm$reject.beta.lx == 1, 1, 0)
container.ldv$reject.lrm.yes.x <- ifelse(container.ldv$reject.lrm.truth == 1 & container.ldv$reject.beta.x == 1, 1, 0)

# = 1 if we don't reject LRM and also don't reject beta.lx/beta.x
container.ardl$reject.lrm.no.lx.no <- ifelse(container.ardl$reject.lrm.truth == 0 & container.ardl$reject.beta.lx == 0, 1, 0)
container.ecm$reject.lrm.no.lx.no <- ifelse(container.ecm$reject.lrm.truth == 0 & container.ecm$reject.beta.lx == 0, 1, 0)
container.ldv$reject.lrm.no.x.no <- ifelse(container.ldv$reject.lrm.truth == 0 & container.ldv$reject.beta.x == 0, 1, 0)

# = 1 if we reject LRM  = truth AND NOT reject beta.lx/beta.x = 0, 0 otherwise
container.ardl$reject.lrm.no.lx <- ifelse(container.ardl$reject.lrm.truth == 1 & container.ardl$reject.beta.lx == 0, 1, 0)
container.ecm$reject.lrm.no.lx <- ifelse(container.ecm$reject.lrm.truth == 1 & container.ecm$reject.beta.lx == 0, 1, 0)
container.ldv$reject.lrm.no.x <- ifelse(container.ldv$reject.lrm.truth == 1 & container.ldv$reject.beta.x == 0, 1, 0)

# collapse everything down:
container.collapse.ardl <- container.ardl %>%
  group_by(Time, e.var, phi, B.lx.true) %>%
  summarize(reject.beta.lx = mean(reject.beta.lx),
            reject.lrm.truth = mean(reject.lrm.truth),
            reject.lrm.yes.lx = mean(reject.lrm.yes.lx),
            reject.lrm.no.lx = mean(reject.lrm.no.lx),
            reject.lrm.no.lx.no = mean(reject.lrm.no.lx.no))

container.collapse.ecm <- container.ecm %>%
  group_by(Time, e.var, phi, B.lx.true) %>%
  summarize(reject.beta.lx = mean(reject.beta.lx),
            reject.lrm.truth = mean(reject.lrm.truth),
            reject.lrm.yes.lx = mean(reject.lrm.yes.lx),
            reject.lrm.no.lx = mean(reject.lrm.no.lx),
            reject.lrm.no.lx.no = mean(reject.lrm.no.lx.no))

container.collapse.ldv <- container.ldv %>%
  group_by(Time, e.var, phi, B.lx.true) %>%
  summarize(reject.beta.x = mean(reject.beta.x), 
            reject.lrm.truth = mean(reject.lrm.truth),
            reject.lrm.yes.lx = mean(reject.lrm.yes.x), # need to label this as lx for appending, even though it's x
            reject.lrm.no.lx = mean(reject.lrm.no.x),
            reject.lrm.no.lx.no = mean(reject.lrm.no.x.no)) # need to label this as lx for appending, even though it's x

# need to combine all the model datasets since geom_bar doesn't work on separate datasets
container.collapse.ardl$model.type <- "ARDL"
container.collapse.ecm$model.type <- "ECM"
container.collapse.ldv$model.type <- "LDV"

# create appended dataset for LR
# short run: time (1), e.var (2), phi (3), B.lx.true (4), reject.lrm.truth (6), reject.lrm.yes.lx (7), reject.lrm.no.lx (8), reject.lrm.no.lx.no (9), model.type (10)
container.collapse.all.LR <- rbind(container.collapse.ardl[c(1,2,3,4,6,7,8,9,10)], container.collapse.ecm[c(1,2,3,4,6,7,8,9,10)], container.collapse.ldv[c(1,2,3,4,6,7,8,9,10)])
container.collapse.all.LR$Time <- as.factor(container.collapse.all.LR$Time)
container.collapse.all.LR$e.var <- as.factor(container.collapse.all.LR$e.var)
container.collapse.all.LR$phi <- as.factor(container.collapse.all.LR$phi)
container.collapse.all.LR$B.lx.true <- as.factor(container.collapse.all.LR$B.lx.true)
container.collapse.all.LR$mc.type[container.collapse.all.LR$phi == -.8 & container.collapse.all.LR$B.lx.true == 1] <- "Alpha = -0.8, Lag X effect = 1"
container.collapse.all.LR$mc.type[container.collapse.all.LR$phi == -.8 & container.collapse.all.LR$B.lx.true == -1] <- "Alpha = -0.8, Lag X effect = -1"
container.collapse.all.LR$mc.type[container.collapse.all.LR$phi == -.2 & container.collapse.all.LR$B.lx.true == 1] <- "Alpha = -0.2, Lag X effect = 1"
container.collapse.all.LR$mc.type[container.collapse.all.LR$phi == -.2 & container.collapse.all.LR$B.lx.true == -1] <- "Alpha = -0.2, Lag X effect = -1"
table(container.collapse.all.LR$mc.type)

# create plots:
# as a proportion out of all times we would have correctly covered the LRE:
container.collapse.all.LR$prop.miss.pctcorrectcov <- container.collapse.all.LR$reject.lrm.no.lx.no/(1 - container.collapse.all.LR$reject.lrm.truth)

p1 <- ggplot(data = subset(container.collapse.all.LR, e.var == 1), aes(x = model.type, y = prop.miss.pctcorrectcov, fill = Time)) + geom_bar(stat = "identity", position = position_dodge()) + theme_minimal() + scale_fill_brewer(palette="Oranges")  + ylab("Proportion Missed (out of correct coverage)") + xlab("Model") + ggtitle("Long-Run, sigma^2_y = 1") + facet_wrap(~mc.type) # we get some missings b/c dividing by 0 for LDV

p2 <- ggplot(data = subset(container.collapse.all.LR, e.var == 5), aes(x = model.type, y = prop.miss.pctcorrectcov, fill = Time)) + geom_bar(stat = "identity", position = position_dodge()) + theme_minimal() + scale_fill_brewer(palette="Oranges") +  ylab("Proportion Missed (out of correct coverage)") + xlab("Model") + ggtitle("Long-Run, sigma^2_y = 5") + facet_wrap(~mc.type) 

pdf("yi1-xi1-related-emwproposal.pdf", width = 1.618*7, height = 7)
grid.arrange(p1, p2, ncol = 1)
dev.off()
